We construct the 1D $\mathbb{Z}_3$ parafermionic model based on the solution of Yang-Baxter equation and express the model by three types of fermions. It is shown that the $\mathbb{Z}_3$ parafermionic chain possesses both triple degenerate ground states and non-trivial topological winding number. Hence, the $\mathbb{Z}_3$ parafermionic model is a direct generalization of 1D $\mathbb{Z}_2$ Kitaev model. Both the $\mathbb{Z}_2$ and $\mathbb{Z}_3$ model can be obtained from Yang-Baxter equation. On the other hand, to show the algebra of parafermionic tripling intuitively, we define a new 3-body Hamiltonian $\hat{H}_{123}$ based on Yang-Baxter equation. Different from the Majorana doubling, the $\hat{H}_{123}$ holds triple degeneracy at each of energy levels. The triple degeneracy is protected by two symmetry operators of the system, $ω$ -parity $P$ ( $ω=e^{{\textrm{i}\frac{2π}{3}}}$ ) and emergent parafermionic operator $Γ$ , which are the generalizations of parity $P_{M}$ and emergent Majorana operator in Lee-Wilczek model, respectively. Both the $\mathbb{Z}_3$ parafermionic model and $\hat{H}_{123}$ can be viewed as SU(3) models in color space. In comparison with the Majorana models for SU(2), it turns out that the SU(3) models are truly the generalization of Majorana models resultant from Yang-Baxter equation.We construct the 1D $\mathbb{Z}_3$ parafermionic model based on the solution of Yang-Baxter equation and express the model by three types of fermions. It is shown that the $\mathbb{Z}_3$ parafermionic chain possesses both triple degenerate ground states and non-trivial topological winding number. Hence, the $\mathbb{Z}_3$ parafermionic model is a direct generalization of 1D $\mathbb{Z}_2$ Kitaev model. Both the $\mathbb{Z}_2$ and $\mathbb{Z}_3$ model can be obtained from Yang-Baxter equation. On the other hand, to show the algebra of parafermionic tripling intuitively, we define a new 3-body Hamiltonian $\hat{H}_{123}$ based on Yang-Baxter equation. Different from the Majorana doubling, the $\hat{H}_{123}$ holds triple degeneracy at each of energy levels. The triple degeneracy is protected by two symmetry operators of the system, $ω$-parity $P$($ω=e^{{\textrm{i}\frac{2π}{3}}}$) and emergent parafermionic operator $Γ$, which are the generalizations of parity $P_{M}$ and emergent Majorana operator in Lee-Wilczek model, respectively. Both the $\mathbb{Z}_3$ parafermionic model and $\hat{H}_{123}$ can be viewed as SU(3) models in color space. In comparison with the Majorana models for SU(2), it turns out that the SU(3) models are truly the generalization of Majorana models resultant from Yang-Baxter equation.

arXiv:1507.05269Jul 19, 20151 citation

SU(2) WZW and parafermion models on the torus

T. Jayaraman, Kumar S Narain, M.H. Sarmadi

Nuclear Physics BOct 1, 199036 citations

ℤ3 parafermionic chain emerging from Yang-Baxter equation

Li-Wei Yu, Mo‐Lin Ge

We construct the 1D ℤ3 parafermionic model based on the solution of Yang-Baxter equation and express the model by three types of fermions. It is shown that the ℤ3 parafermionic chain possesses both triple degenerate ground states and non-trivial topological winding number. Hence, the ℤ3 parafermionic model is a direct generalization of 1D ℤ2 Kitaev model. Both the ℤ2 and ℤ3 model can be obtained from Yang-Baxter equation. On the other hand, to show the algebra of parafermionic tripling intuitively, we define a new 3-body Hamiltonian H123 based on Yang-Baxter equation. Different from the Majorana doubling, the H123 holds triple degeneracy at each of energy levels. The triple degeneracy is protected by two symmetry operators of the system, ω-parity P [formula in text] and emergent parafermionic operator Γ, which are the generalizations of parity PM and emergent Majorana operator in Lee-Wilczek model, respectively. Both the ℤ3 parafermionic model and H123 can be viewed as SU(3) models in color space. In comparison with the Majorana models for SU(2), it turns out that the SU(3) models are truly the generalization of Majorana models resultant from Yang-Baxter equation.We construct the 1D ℤ3 parafermionic model based on the solution of Yang-Baxter equation and express the model by three types of fermions. It is shown that the ℤ3 parafermionic chain possesses both triple degenerate ground states and non-trivial topological winding number. Hence, the ℤ3 parafermionic model is a direct generalization of 1D ℤ2 Kitaev model. Both the ℤ2 and ℤ3 model can be obtained from Yang-Baxter equation. On the other hand, to show the algebra of parafermionic tripling intuitively, we define a new 3-body Hamiltonian H123 based on Yang-Baxter equation. Different from the Majorana doubling, the H123 holds triple degeneracy at each of energy levels. The triple degeneracy is protected by two symmetry operators of the system, ω-parity P [formula in text] and emergent parafermionic operator Γ, which are the generalizations of parity PM and emergent Majorana operator in Lee-Wilczek model, respectively. Both the ℤ3 parafermionic model and H123 can be viewed as SU(3) models in color space. In comparison with the Majorana models for SU(2), it turns out that the SU(3) models are truly the generalization of Majorana models resultant from Yang-Baxter equation.

Scientific ReportsFeb 23, 201610 citations

Spinon basis for higher level SU(2) WZW models

Peter Bouwknegt, Andreas W. W. Ludwig, Kareljan Schoutens

arXiv:hep-th/9412108Physics Letters BOct 1, 199560 citations

Application of su(2) algebra

Guozhen Wu

Elsevier eBooksJan 1, 20050 citations

\mathbb{Z}_3

Parafermionic Chain Emerging From Yang-Baxter Equation

We construct the 1D

\mathbb{Z}_3

parafermionic model based on the solution of Yang-Baxter equation and express the model by three types of fermions. It is shown that the

\mathbb{Z}_3

parafermionic chain possesses both triple degenerate ground states and non-trivial topological winding number. Hence, the

\mathbb{Z}_3

parafermionic model is a direct generalization of 1D

\mathbb{Z}_2

Kitaev model. Both the

\mathbb{Z}_2

and

\mathbb{Z}_3

model can be obtained from Yang-Baxter equation. On the other hand, to show the algebra of parafermionic tripling intuitively, we define a new 3-body Hamiltonian

\hat{H}_{123}

based on Yang-Baxter equation. Different from the Majorana doubling, the

\hat{H}_{123}

holds triple degeneracy at each of energy levels. The triple degeneracy is protected by two symmetry operators of the system,

ω

-parity

P

(

ω=e^{{\textrm{i}\frac{2π}{3}}}

) and emergent parafermionic operator

Γ

, which are the generalizations of parity

P_{M}

and emergent Majorana operator in Lee-Wilczek model, respectively. Both the

\mathbb{Z}_3

parafermionic model and

\hat{H}_{123}

can be viewed as SU(3) models in color space. In comparison with the Majorana models for SU(2), it turns out that the SU(3) models are truly the generalization of Majorana models resultant from Yang-Baxter equation.